Nonlinear Chirp Research Articles

A novel variational nonlinear chirp mode decomposition-based critical brain-region investigation for automatic emotion recognition

The field of affective computing that deals with emotion recognition from physiological information, particularly electroencephalography (EEG), is becoming more and more important. Researchers have employed these signals to identify emotions, but the majority of them only distinguish a limited number of emotional states (e.g. happiness, fear, sadness, calmness, anger, etc.). This study outlines the proposed model for classifying nine emotional states from the DREAMER database into arousal, valence, and dominance dimensions using a discrete scale. To create it, we studied variational non-linear chirp mode decomposition (VNCMD) to decompose the EEG signals into five distinct modes. 11 entropy features were extracted from each mode. Then a comparative analysis of six popular machine learning-based classifiers was performed. The VNCMD's third mode with a rotational random forest classifier gave the best performance parameters for this application. This systematic analysis revealed that the best brain region, i.e., the anterior frontal area using only 2 channels, provided the highest accuracy and F1-score for arousal: 96.07% and 97.30%, valence: 94.49% and 95.58%, and dominance: 95.83% and 97.19% categories. Results, using the DREAMER dataset, show that our model can have the highest predictive ability with AUCs of 0.98, 0.98, and 0.97 for the arousal, valence, and dominance categories, respectively. The findings of this study demonstrate that the features, brain regions, and machine learning models commonly employed in emotion classification tasks may be used in more difficult tasks, like the prediction of precise values for arousal, valence, and dominance.

Baseband modulational instability and dynamics of rogue waves in coherently coupled Bose–Einstein condensates

We consider coupled dimensionless Gross-Pitaevskii (GP) equations that describes effective coherently coupled Bose–Einstein condensates (BECs) trapped in external complex potentials. Through a modified similarity transformation, the integrability condition is obtained and the system is reduced to one single integrable autonomous cubic-quintic nonlinear Schrödinger (NLS) equation with self-steepening and self-frequency shift. The baseband modulational instability (MI) for the obtained NLS equation is investigated in details. Through the exact first- and second-order rogue wave solutions with nonlinear chirp of the coupled GP equation, we investigate analytically the propagation dynamics of rogue waves on weakly perturbed continuous wave solutions in the parameter space where the baseband MI exist. Our results show that one can manipulate the motion of matter rogue waves by controlling the external trapping potential. Simulations provide supporting evidence that rogue waves can only emerge in regimes where baseband MI occurs. Our results show how multiplet first- and second-order rogue waves can be generated by varying some solution parameters such as the amplitude parameter.

A Modified Range Doppler Algorithm for High-Squint SAR Data Imaging

The high-squint airborne Synthetic Aperture Radar (SAR) has the ability to detect the target area flexibly, and the detection swath is significantly increased compared with the side-looking SAR system. Therefore, it is of great significance to carry out research on high-precision imaging methods for high-squint airborne SAR. However, the high-squint SAR echoes have large Range Cell Migration (RCM), resulting in severe range–azimuth coupling and strong spatial variation. In this paper, a Modified Range Doppler Algorithm (MRDA) is proposed to cope with these effects introduced by the significant RCM in high-squint airborne SAR imaging. The bulk compensation preprocessing is first adopted to remove the considerable RCM and severe cross-coupling in a two-dimensional frequency domain. Then, Non-Linear Chirp Scaling (NLCS) in the range direction is utilized to equalize the range-variant chirp rate caused by the residual RCM and coupling and, therefore, the consistent range phase compensation can be fulfilled in range frequency domain. The modified correlation processing is executed to compensate the residual Doppler phase modulation, the residual RCM and the range-variant cubic phase modulation, which guarantees the characteristics of high efficiency and high precision. The simulations have demonstrated that the MRDA can focus the SAR echoes with large squint angles more effectively than the algorithms based on the Linear Range Walk Correction (LRWC) method.

An Improved UAV Bi-SAR Imaging Algorithm with Two-Dimensional Spatial Variant Range Cell Migration Correction and Azimuth Non-Linear Phase Equalization

The transmitter and receiver of unmanned aerial vehicle (UAV) bistatic synthetic aperture radar (Bi-SAR) are respectively carried on different UAV platforms, which has the advantages of flexible movement and strong concealment, and has broad application prospects in remote sensing fields. However, the range cell migration (RCM) and azimuth non-linear phase (ANP) of UAV Bi-SAR are seriously spatially variant along the range and azimuth directions, while the UAV Bi-SAR has a short operating range, complex trajectory and wide azimuth beam. Aiming at the problem that the RCM and ANP of UAV Bi-SAR in spotlight mode are difficult to correct and equalize due to the severe two-dimensional (2D) spatial variation, an RCM correction (RCMC) and ANP equalization (ANPE) method based on Doppler domain blocking is proposed. First, the azimuth spatial variance of RCM is eliminated by Doppler blocking, and the range spatial variant RCMC is realized by RNCS. Second, by combining Doppler blocking with azimuth nonlinear chirp scaling (ANCS), this method can adapt to ANPE with larger width and more severe spatial variation. At last, the criteria of Doppler blocking are given in detail, and the effectiveness of the proposed method is verified by UAV Bi-SAR real data and computer simulation.

Lamb wave based damage imaging under nonlinear chirp excitation

Considering a trade-off between temporal-spatial resolution and multi-mode nature of Lamb waves, tone bursts with short durations are usually used as excitations in Lamb wave based damage detection. A short-duration excitation usually requires a large amplitude to carry sufficient energy so as to obtain response signals with enough signal-to-noise ratio and cover a large inspection area. In this paper, an alternative Lamb wave damage imaging method using nonlinear chirp (nonlinear frequency modulation, NLFM) excitation with a long duration and a small amplitude is proposed. The signal processing techniques of pulse compression and dispersion compensation are adopted to compress the long-duration wave packets of response signals into short ones. Compared with conventional tone burst excitations with short durations and small amplitudes, due to the long duration of the nonlinear chirp excitation and the use of pulse compression, sufficient energy can be applied to transducers under small amplitude excitations so the image contrast in imaging will not degrade. Furthermore, as large amplitude excitations are no longer required, high voltage amplifiers are not necessary so the hardware of the Lamb wave testing system is simplified. Experiments on a carbon steel plate with an artificial crack are carried out and Lamb wave signals are collected using a linear array consisting of nine PZTs. Experimental results under the NLFM signal and conventional tone bursts are provided. Experimental results show that under the condition of the same excitation amplitude, the proposed method under the NLFM excitation can achieve better imaging quality compared with methods under conventional tone bursts.

A New Method for Separating Temperature Effect of Bridge Strain Monitoring

Temperature has a significant influence on bridge strain monitoring data. To improve the accuracy of temperature effect separation in strain monitoring data, this paper proposes a temperature effect separation method comprising variational nonlinear chirp mode decomposition (VNCMD), principal component analysis (PCA) and blind source separation. Firstly, VNCMD was used to decompose the monitoring data of strain and temperature, and the intrinsic mode functions (IMF) of strain and temperature signals were obtained. Secondly, PCA was used to reduce the dimension of IMF, and the false components were eliminated to select the optimal components. After reducing the dimension, the components were used as the input of fast independent component analysis model for blind source separation. Finally, the feasibility and accuracy of the method was verified via the signal-to-noise ratio (SNR) in the simulated signal, and the separation results were evaluated using the Pearson correlation coefficient between the strain component and the corresponding temperature component in real bridge monitoring data. The proposed method performed better than the empirical mode decomposition (EMD) method. The signal-to-noise ratio (SNR) of VNCMD improved 51.80% for daily temperature difference effect and 32.41% for annual temperature difference effect in the numerical study, respectively; the correlation coefficients of VNCMD improved 52.90% for daily temperature difference effect and 4.26% for annual temperature difference effect in practical verification, respectively.

Linearization of an Electron Beam’s Longitudinal Phase Space Using a Hollow-Channel Plasma

The removal of undesired beam nonlinear energy chirp (time-energy correlation) or linearization of the beam longitudinal phase space (LPS) is crucial for high-brightness linac-based scientific applications, such as x-ray free-electron lasers. In this paper, we propose that a low-density hollow channel plasma can be used as a near-ideal passive linearizer to significantly linearize the beam LPS and, at the same time, preserve the beam emittance. Physically, the passage of the beam through the hollow plasma channel excites a strong quasicosinoidal longitudinal wakefield that acts to mitigate the beam nonlinear energy chirp by superimposing a reverse chirp on the beam. The theoretical analyses and large-scale three-dimensional start-to-end simulations confirm that the beam longitudinal phase space can be almost completely linearized without noticeable beam emittance growth. Application of such a near-ideal linearizer may significantly improve the performance of numerous accelerator-based applications.

A Monostatic Forward-Looking Staring Spotlight SAR Raw Data Generation and Hybrid-Domain Image Formation Modifications Based on Extended Azimuth Nonlinear Chirp Scaling Autofocusing

Forward-looking staring spotlight synthetic aperture radar (FSS-SAR) offers operational advantages over conventional squinted SAR counterparts. However, due to its complex observation configuration, pixel anomalies occur when processing raw data. For instance, in the forward-looking geometry, symmetrically distributed point scatterers along the flight path have the same Doppler history, resulting in azimuth ambiguities, whereas staring observation narrows and skews the 2D received spectrum, reducing signal orthogonality and causing spectral folding. As a result, not only is the Doppler frequency gradient too small to be precisely measured in the FSS-SAR mode, limiting the ability to achieve high azimuth angular resolution, but it also suffers from azimuth ambiguities when forming an image. To overcome such azimuth-variant characteristics known as inherent resolutional anomalies, a hybrid-domain image formation algorithm (IFA) based on azimuth scaling is modified here. As an approach, radiometric bias correction (RBC) techniques in conjunction with an extended azimuth nonlinear chirp scaling (ANCS) algorithm capable of equalizing range space variance in the azimuth direction, which benefits from an embedded autofocusing step, have been designed for raw data processing. Given the fact that the platform experiences trajectory deviations under a real-flight condition compared to an ideal trajectory, a pre-processing motion compensation (MOCO) step based on Kalman filtering is included within the IFA. The entire proposed IFA solution tackled the inherent resolutional anomalies of FSS-SAR and succeeded in reconstructing the focused image without azimuthal anomalies. To further assess the IFA, a modified Cartesian back-projection (BP) algorithm was developed along with other objective evaluation scenarios, all of which confirm that the proposed hybrid-domain extended ANCS algorithm is valid for the FSS-SAR application.

Chirped nonlinear waves in the cubic-quintic distributed nonlinear Schrödinger equation with external trap, self-steepening and self-frequency shift

A cubic-quintic inhomogeneous nonautonomous nonlinear Schrödinger (NLS) equation with an external trap, self-steepening, and self-frequency shift that models the transmission of nonlinear waves in nonautonomous inhomogeneous systems is considered. The integrability conditions under which the equation is converted into the standard NLS equation are obtained and a variety of nonlinear wave solutions with nonlinear chirping such as one-soliton solution, two-soliton solution, Akhmediev breather (AB) solution, Ma breather (MB) solution, as well as first- and second-order rogue wave (RW) solution are reported. We show how various parameters of either the model equation or the solutions may affect the nature of nonlinear waves with their frequency chirps propagating in nonautonomous inhomogeneous systems modeled by the NLS equation under consideration. The density profiles of nonlinear waves obtained from all these solutions are analyzed. These solutions are used for investigating analytically the dynamics of nonlinear waves in Bose-Einstein condensates (BECs) with both two- and three-body interatomic interactions when the gain/loss of atoms is taken into consideration. Considering BEC systems with time-independent trap frequency, we show that under a constant gain/loss parameter, the trap parameter can be used to convert triplet second-order RWs into either doublet second-order RWs or a composite of one bright solitary wave and a doublet second-order RWs. Also, our results reveal that for BECs with constant trap frequency under kink-like gain/loss parameter, the trap parameter can be used to convert (i) triplet second-order RWs into single second-order RWs, and (ii) two-soliton into doublet rogue wave. The family of chirped nonlinear wave solutions presented in this work may prove significance for designing the manipulation and transmission of nonlinear waves. Also, the found here results may provide possibilities to manipulate experimentally some nonlinear waves such as rogue waves or two-soliton in BEC systems.

Chirping instabilities produced by a runaway electron beam at a spherical tokamak

Two different types of MHD instabilities with rapidly chirping frequency were found to arise in the Globus-M2 spherical tokamak in substantially different frequency ranges. The first type arises at frequencies of an order of 1 MHz in ohmic plasmas at relatively low density in a wide range of toroidal magnetic fields and plasma currents. This type of instability was identified as compressional Alfvén waves, driven by electrons, accelerated during a sawtooth crush. It was found that the mode frequency is sweeping in time, according to the Berk–Breizman hole–clump nonlinear chirping model. The second type of wave arises in a specific single-swing regime of the central solenoid current with a very narrow plasma column, when the plasma tends to decay at extremely low density and, in fact, is an instability of the runaway electron beam. The exited modes cover the whole observed frequency range and are divided into several (two or three) frequency regions: approximately 0–30 MHz, 60–120 MHz and sometimes 30–60 MHz. Reconnection of the branches was also observed. Single chirps are more rapid than for 1 MHz Alfvén instability and follow an exponential law. This paper, to our knowledge, is the first report of frequency chirping instabilities excited by accelerated electrons at a spherical tokamak.

A Modified NLCS Algorithm for High-Speed Bistatic Forward-Looking SAR Focusing with Spaceborne Illuminator

The coupling and spatial variation of range and azimuth parameters is the biggest challenge for bistatic forward-looking SAR (BFSAR) imaging. In contrast with the monostatic SAR and translational invariant bistatic SAR (TI-BSAR), the range cell migration (RCM), and Doppler parameters of high-speed bistatic forward-looking SAR (HS-BFSAR) have two-dimensional spatial variation characteristics, which makes it difficult to obtain SAR images with satisfactory global focusing. Firstly, based on the configuration of the spaceborne illuminator and high-speed forward-looking receiving platform, the accurate range-Doppler domain expression of the echo signal is derived in this paper. Secondly, using this analytical expression, a range nonlinear chirp scaling (NLCS) is proposed to equalize the RCM and equivalent range frequency modulation (FM) rate so that they can be uniformly processed in the two-dimensional frequency domain. Next, in the azimuth processing, the proposed method decomposes the Doppler contribution of the transmitter and receiver, respectively. Then, an azimuth NLCS is used to eliminate the spatial variation of the azimuth FM rate. Finally, a range-dependent azimuth filter is constructed to achieve azimuth compression. Simulation results validate the efficiency and effectiveness of the proposed algorithm.

Wakefield Generation and Enhancement of Electron Energy to the Multi-GeV in a Magnetized Plasma

The nonlinear interaction of an intense chirped laser pulse with transversely magnetized plasma is studied theoretically. The work described in this investigation is dealing with the characteristics of the wakefield generation by different chirping functions. Numerical results reveal that the amplitude and wavelength of the generated wakefield are highly influenced by the chirping constant and types of chirping function. Moreover, for the linear chirping function the positive chirping constant and for the nonlinear chirping functions the negative chirping constants excite larger wake amplitudes. In addition, it was found that by choosing a proper chirping constant for each chirping functions, one could obtain highly GeV electron energy gain. The maximum energy is obtained for the electron injected in the wakefield induced by the Exp and Linear chirped pulse. The maximum electron energy is about 2.5 GeV for the wake excited by the negative Exp chirp function. Further results revealed that the energy of the electron is significantly enhanced using an external transverse magnetic field.

Improved ship imaging algorithm for geosynchronous synthetic aperture radar (SAR) featured by subaperture time window selection optimization and inverse SAR translational compensation

An inverse synthetic aperture radar processing-based algorithm is improved for ship imaging in geosynchronous synthetic aperture radars (GEO SARs) to solve the technical challenges including long accumulation time and complex target motion characteristics. The improvement on the existing algorithm mainly involves four aspects. First, the formula for calculating the appropriate time length of subaperture is derived, according to the principle that the accumulated power of the ship’s echo corresponding to the subaperture duration ensures that the signal-to-noise ratio satisfies the requirement of GEO SARs. The derived formula solves the problem that how long the subaperture length should be taken with regards to a long accumulation time of GEO SAR when imaging ships. Second, we propose an optimization criterion for determining the appropriate subaperture time window by ensuring that the maximum number of ship pixels is detected in the subaperture image. The proposed criterion is used to optimize the location of the subaperture time window in the long accumulation time. Third, the SPECAN algorithm used in the scene imaging process is replaced by an improved nonlinear chirp scaling (NLCS) algorithm to improve the imaging accuracy of the scene. Our improvement on the traditional NLCS algorithm focuses on improving precisions of some of the formulas in the traditional algorithm. Furthermore, a translational compensation algorithm is proposed by considering the influence of spatial variance of slant range history of GEO SARs. The proposed translational compensation algorithm improves the compensation accuracy since the spatial variance of different scatterers in the scene is considered. A series of simulation experiments related with ship imaging in GEO SARs were carried out to verify the correctness of the proposed algorithm and the improvement on the imaging quality compared with that of the existing algorithm.

Continuously tunable high photon flux high harmonic source.

In this work, a continuously tunable extreme ultraviolet source delivering a state-of-the-art photon flux of >1011 ph/s/eV spanning from 50 eV to 70 eV is presented. The setup consists of a high-power fiber laser with a subsequent multipass cell followed by a waveguide-based high harmonic generation setup. Spectral tuning over the full line spacing is achieved by slightly adjusting the lasers driving pulse energy, utilizing nonlinear propagation effects and pulse chirping. The presented method enables a high tuning speed while delivering reproducible and reliable results due to a simple experimental realization. For possible future experiments, a method for continuous, on-demand pulse-to-pulse switching of the generated XUV radiation with full spectral coverage is conceived.

Nonlinear frequency chirps from a stabilized injected phase-modulated fiber laser loop

A phase-modulated frequency-shifting loop is injected by a single-frequency laser at 1.5 μm. In so-called Talbot conditions, i.e., when the modulation frequency is an integer multiple of the inverse of the cavity round-trip time, the loop generates a frequency comb whose temporal trace consists in a train of pulse doublets whose positions in time depend on the frequency of the injection laser. When the modulation frequency is slightly detuned from the Talbot condition, nonlinear frequency chirps are predicted and observed in the output pulse train. We demonstrate that these nonlinear chirps are not restricted to sinusoidal shapes, and also that the loop can be stabilized by exploiting the intracavity phase modulation.

An Extended Frequency Scaling Algorithm for Bistatic SAR With High Squint Angle

Bistatic synthetic aperture radar (BiSAR) is an extended and complementary observation method to conventional monostatic SAR remote sensing. When high range and azimuth resolution are required in BiSAR, the transmitting platform, i.e., the LEO satellite, should work in the spotlight or sliding spotlight mode, which means a wide bandwidth Chirp signal is transmitted, and the targets are illuminated for a long enough time as well. In order to reduce the sampling frequency in the receiving system and improve the efficiency of the focusing procedure for this BiSAR configuration, the echoes should be dechirp received. A bistatic extended frequency scaling algorithm (Bi-EFSA) is proposed in this paper to deal with the dechirp received bistatic SAR echoes. The first step of Bi-EFSA is the range walk correction in the 2-D time domain, which reduces the space variance of the range curvatures and removals the serious coupling between range and azimuth caused by the high squint angle. After that, the range compression is achieved by secondary range compression (SRC) and bulk shift. Then, the space variance of the azimuth frequency modulation rate, introduced by the range walk correction step, is corrected by implementing the azimuth nonlinear chirp scaling (ANCS) operation. Following this, the focused results in the range frequency and azimuth time domain are obtained by the azimuth compression. The point targets and extended-scene simulations validate the effectiveness of the proposed algorithm.

Focusing of Wide-Swath Range Sweep SAR With Extended Wide Nonlinear Chirp Scaling Algorithm

Multi-channel, DBF-based high-resolution wide swath SAR (HRWS-SAR) is dedicated to acquiring large observation width and high resolution in a single pass. However, the existing HRWS-SAR imaging modes are difficult to cover effectively for the coastline area not parallel to the satellite orbit. Combined with the beam direction changing, variable PRI and distance-oriented DBF techniques, the wide-swath range sweep SAR (WRS-SAR) can image the wide coastline area not parallel to the satellite orbit at high resolution in a single-pass. In this study, an extended wide nonlinear chirp scaling (E-WLNCS) algorithm is proposed, which mainly consists of: a time-domain blind range sample reconstruction algorithm combined with phase variation estimation, a non-uniform resampling algorithm combined with Doppler variation correction, and the effectiveness of the proposed modified E-WLNCS algorithm is demonstrated through point target and surface target simulations.

Focus Improvement of Spaceborne-Missile Bistatic SAR Data Using the Modified NLCS Algorithm Based on the Method of Series Reversion

The speed and direction of a missile shifts sharply in the dive phase, making the azimuth frequency modulation (FM) rate change with the azimuthal position, leading to azimuth ambiguities and image distortion. To solve this problem, a modified nonlinear chirp scaling (NLCS) algorithm was adopted to compensate for the azimuth FM rate. First, the geometric configuration and echo signal model of the spaceborne missile bistatic synthetic aperture radar (SAR) were built, and then the Doppler frequency correction was performed, and the 2-D spectrum of the signal was derived by the method of series reversion. Next, range migration correction and range compression were finished in the 2-D frequency domain. Following this, a modified NLCS algorithm was proposed to solve the space variance of Doppler phase problem. After compensating for the azimuth FM rate, the azimuth compression focusing was completed and the imaging result was obtained. Finally, by comparing the calculation amount, imaging effect, and performance index with the traditional NLCS algorithm, it can be concluded that the algorithm reduced the calculation amount by 1.0128 × 108 floating point operations per second (FLOPs) compared with the traditional NLCS algorithm, and the azimuth focusing effect of the edge point was greatly improved. Its resolution, peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR) were improved by 0.87 m, 3.32 dB, and 1.79 dB, respectively, which proved the effectiveness and feasibility of this method.

Chirped localized pulses in a highly nonlinear optical fiber with quintic non-Kerr nonlinearities

We study the existence and propagation properties of chirped localized pulses in a highly nonlinear fiber medium exhibiting self-steepening, self-frequency shift, and quintic non-Kerr nonlinearities. Pulse evolution in such fiber system is governed by a higher-order nonlinear Schrödinger equation incorporating the derivative Kerr and non-Kerr nonlinear terms. We show that bright, dark and kink type solitary waves exist in the presence of all physical processes. A special ansatz is introduced to analyze the existence of solitary waves on a continuous-wave background in the optical fiber medium. It is shown that the obtained localized pulses exhibit a nonlinear chirp which has a quadratic dependence on light intensity. We also find that the magnitude of the associated frequency chirp can be controlled effectively by varying the parameters of self-steepening, self-frequency shift, and derivative non-Kerr nonlinearity effects. The restrictions on the optical fiber parameters are also extracted for the existence of these nonlinearly chirped solitary waves. Results in this study may be useful for experimental realization of shape-preserved pulses in optical fibers and further understanding of their optical transmission properties.

Nonlinear frequency chirping and radial restructure of the ion-temperature-gradient-driven turbulence

Global nonlinear gyrokinetic simulation of the ion-temperature-gradient (ITG) modes clearly demonstrates the nonlinear phase-space resonance, which can be well understood by the nonlinear frequency chirping due to the nonlinear poloidal acceleration of resonant particles by the large-scale structure of radial electric field rather than the widely discussed local shearing effects of the zonal flows. The nonlinear radial restructure of a single-n ITG mode generates multiple daughter-ballooning-modes.